pseudo-wild numbers

N. J. A. Sloane njas at
Mon Jan 15 00:33:28 CET 2001

The following is an attempt at producing a sequence
which behaves like the Wild Numbers described by Enoch Haga
in his recent posting.  The idea is to find a map f from
rationals to rationals that occasionally produces an integer.
One starts at n = n/1, and iterates f until an integer is reached.
That integer is a(n).  If no integer is reached,
a(n) is defined to be zero.

%I A058971
%S A058971 3,2,6,3,3,4,10,87,6,6,9,7,6,6,87,9,6,10,7,8,9,12,9,15,12,10,16,15,
%T A058971 9,16,12,12,15,12,87,19,15,14,19,21,12,22,14,13,18,24,34,19,12,18
%N A058971 For a rational number p/q let f(p/q) = sum of divisors of p+q divided
 by number of divisors of p+q; a(n) is obtained by iterating f, starting at n/1,
 until an integer is reached, or if no integer is ever reached then a(n) = 0.
%O A058971 1,1
%K A058971 nonn,easy,more
%p A058971 with(numtheory); f:=proc(n) if whattype(n) = integer then sigma(n+1)/
sigma[0](n+1) else sigma(numer(n)+denom(n))/sigma[0](numer(n)+denom(n)); fi; end
%A A058971 njas, Jan 14 2001
%e A058971 1 -> (1+2)/2 = 3/2 -> (1+5)/2 = 3, so a(1) = 3.

Obviously many similar examples could be constructed.
Perhaps it will be possible to find one that comes
close to matching A058883, which is supposed to have
this kind of definition.


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